Soft body for a round character
You can use the To Sphere transformation to make sets of vertices more nearly spherical: https://docs.blender.org/manual/en/latest/modeling/meshes/editing/transform/to_sphere.html

You can also use Smooth Vertex to smooth out sets of vertices, as unintended jaggedness is a common problem when trying to achieve smooth features in a complex mesh:

https://blenderartists.org/t/is-there-a-way-to-smooth-out-the-vertices-in-blender/518443

I would, however, add this: when a key feature of a primitive form (like sphericity) is desired, it is usually best to start from a primitive (like, well, a sphere) that already has that form, and only gradually modify those features of it that you don't want to maintain. Working in the opposite direction (complex form to primitive features) is often considerably more difficult.